SOLUTION: calculate the indicated value. f(x) = 14x^2 + 15x - 14 g(x) = 14x^2 + 11x - 10 find f(f(4)) I started by plugging in 4 for x: f(x) = 14(4)^2 + 15(4) - 14=270 Then I put t

Algebra ->  Functions -> SOLUTION: calculate the indicated value. f(x) = 14x^2 + 15x - 14 g(x) = 14x^2 + 11x - 10 find f(f(4)) I started by plugging in 4 for x: f(x) = 14(4)^2 + 15(4) - 14=270 Then I put t      Log On


   

Question 84015: calculate the indicated value.
f(x) = 14x^2 + 15x - 14
g(x) = 14x^2 + 11x - 10
find f(f(4))
I started by plugging in 4 for x:
f(x) = 14(4)^2 + 15(4) - 14=270
Then I put that in for x:
f(x) = 14(270)^2 + 15(270) - 14=10210036
However, I asked about this question once and was told the answer was:
f[f(4)] = f[14*4^2+15*14-1]
=f[420]
=14*420^2 + 15*420-14
=2,469,796
I am sure this is the correct answer but I'm just wondering what I'm doing wrong to not come to this answer. I am confused by this step:
f[f(4)] = f[14*4^2+15*14-1]
I dont understand why its 15*4 instead of 15*4, and why its -1 and not -14. Thank you for the help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets first find f%284%29 which is the inner function

f%284%29=14x%5E2+%2B+15x+-+14 Start with the given equation

f%284%29=14%284%29%5E2+%2B+15%284%29+-+14 Plug in x=4

f%284%29=14%2A16+%2B+15%2A4+-+14Square 4

f%284%29=224+%2B+60+-14 Multiply

f%284%29=270 Combine like terms

Since f%284%29=270 f%28f%284%29%29=f%28270%29

So lets find f%28270%29

f%28270%29=14x%5E2+%2B+15x+-+14 Start with the given equation

f%28270%29=14%28270%29%5E2+%2B+15%28270%29+-+14 Plug in x=270

f%28270%29=14%2A72900+%2B+15%2A270+-+14 Square 270

f%28270%29=1020600+%2B+4050+-14 Multiply

f%28270%29=1024636 Combine like terms

So f%28f%284%29%29=1024636

You are right, it should be 15*4-14. So that led to the wrong answer. As for your answer, I'm not sure what you messed up on. The best way to check these problems is to graph and use the composite function feature (as I'm doing) to verify your answer.